Question

On selling a mobile phone for $Rs\,750$, a shopkeeper loses $10\% $. For what amount should he sell it to gain $5\% $ ?

Answer 1

Hint: The given question revolves around the topic and concepts of profit and loss. The question deals with first purchasing some goods at a cost price, then selling the goods at a selling price incurring a loss of $10\% $ in the transaction. So, we have to find the price at which the phone should have been sold for a gain of $5\% $. So, we will first consider the cost price to be x and then find the loss incurred by finding $10\% $ of the cost price of the item. Then, we will find the selling price of the item in terms of variable x and equate it to the given amount to find the value of variable x.

Complete step-by-step solution:
So, let us assume the cost price of the item is Rs x.
Now, we have the loss percent as $10\% $.
So, we calculate the loss percent by calculating $10\% $ of the cost price.
So, $10\%$ of x is $\dfrac{{10}}{{100}} \times \left( {Rs\,x} \right)$.
We cancel the common factors in numerator and denominator.
Hence, the loss incurred in the transaction is $Rs\,\dfrac{x}{{10}}$.
Now, since we have incurred a loss in the whole transaction. So, we have the formula ${\text{Selling Price = }}\left( {{\text{Cost}}{\text{Price}}} \right) - \left( {{\text{Loss}}} \right)$
So, we get the selling price as ${\text{Selling Price = }}\left( {\text{x}} \right) - \left( {\dfrac{x}{{10}}} \right)$
Taking LCM and simplifying the expression, we get,
$ \Rightarrow {\text{Selling Price = }}\left( {\dfrac{{10x - x}}{{10}}} \right)$
$ \Rightarrow {\text{Selling Price = }}\left( {\dfrac{{9x}}{{10}}} \right)$
Now, we are given the selling price of the item as $Rs\,750$. Equating both, we get,
$\left( {\dfrac{{9x}}{{10}}} \right) = 750$
Using the rule of transposition and shifting the terms in the equation, we get,
\[ \Rightarrow x = 750 \times \dfrac{{10}}{9}\]
Simplifying the calculation, we get,
\[ \Rightarrow x = \dfrac{{7500}}{9}\]
So, the cost price of the mobile is \[Rs\,\dfrac{{7500}}{9}\].
 Now, we calculate the $5\% $ gain over the cost price of the mobile.
So, we get, Gain $ = \dfrac{5}{{100}} \times \left( {Rs\,\dfrac{{7500}}{9}} \right)$
Simplifying the expression, we get,
$ = Rs\,5 \times \dfrac{{75}}{9}$
Simplifying the calculations, we get,
$ = Rs\,\dfrac{{385}}{9}$
Now, calculating the selling price of the mobile for $5\% $ gain using the formula \[\left( {{\text{Cost Price}}} \right){\text{ + }}\left( {{\text{Gain}}} \right){\text{ = }}\left( {{\text{Selling}}\,{\text{Price}}} \right)\], we get,
Selling Price $ = Rs\,\dfrac{{7500}}{9} + Rs\,\dfrac{{385}}{9}$
Simplifying the calculations, we get,
$ = Rs\,\left( {\dfrac{{7500 + 385}}{9}} \right)$
$ = Rs\,\dfrac{{7885}}{9}$
Cancelling common factors in numerator and denominator, we get,
$ = Rs\,875$
So, the mobile should be sold for $Rs\,875$ to gain $5\% $ on the transaction.

Note: One must have accuracy in arithmetic so as to solve these types of questions within a limited time frame. We should have a clear understanding of how to find the percentage of a specific number so as to find the gain and loss percent for the goods. We must know the formula to calculate the selling price when provided with cost price and loss or gain incurred.